You can create a cellar space as "auxilliary storage" for the apartment it is connected to but no living would be allowed on that floor. It's fairly common but no way could it be an entirely separate apartment legally.

: : : : "You don't need one to report this to DoB. Note: no sub-basement can ever legally be used for humans to live in. You can research this yourself in the Building Code, part of the NYC Admin Code, at your library or purchase it at the NYC Store."

: : : : This is not exactly true. There are grey areas, first off a basement and cellar are two different things, do you really know which it is?

: : From the original question: "the actual construction done was a sub-basement conversion into a livable dwelling": He wrote "sub-basement", not "basement" nor "cellar". A sub-basement, which is below a basement, can never be used for human living purposes.

: : : Brownstones and certain areas allow for different circumstances and have different definitions for basements and cellars

: No, they don't. There is one definition for basement, a second definition for cellar.